Why does the mechanism shown below balance when the load applied to each platform is the same, even when the lever arms from the pivot are different?

Unequal loads

Equal load; unequal lever arm

It “looks wrong” but an analysis shows that the applied moment is balanced by the moment in the support rod. One of the Eng-tips respondants came up with an even simpler analysis however, showing without any calculation at all that the mechanism will be in equilibrium for equal loads with any position of the loads:

“Use energy method. By inspection (due to parallelogram) the platforms stay flat during motion. Therefore, vertical displacement at any point on either platform is equal. Same vertical displacement, same potential energy.”